Problema Solution
The sum of the squares of two consecutive even integers is 340. Find the integers.
Answer provided by our tutors
Let n and (n+1) be the integers.
n2 + (n+1)2 = 340
n2 + n2 + 2n + 1 = 340
2n2 + 2n = 339 (subtract 1 from both sides of the equation, collect terms)
2(n2+n) = 339 (factor out 2 for clarity)
This equation has no integer solution for n. If n is an integer, n2 is an integer and (n2+n) is an integer. No integer exists such that multiplying it by 2 will give 339.